The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.

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Thermodynamics and Axioms and the like

Can thermodynamics and any important related information be expressed as a set of axioms with various 'rules of manipulation'?
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48 views

Entropy $S$ for canonical (NVT) and isobaric (NPT) ensemble

In case of non-isolates system (NVT or NPT ensemble), I learned I can calculate the entropy, $$S=-k_B\sum_jp_j\ln(p_j)$$ where $p_j$=probability at $j$ state. but I saw that the entropy is also ...
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55 views

Magnetic susceptibility in ising model as magnetization change

Let's say I have a standard 2D Ising model with $$ H(\sigma) = - \sum_{<i~j>}\sigma_i \sigma_j - h\sum_{j} \sigma_j $$ With the metropolis algorithm, I can compute various things like energy ...
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5answers
431 views

How to understand singularities in physics?

The question is probably two-folded and I will try not to make it too vague, but nonetheless the question remains general. First fold: In most physical laws, that we have analytic mathematical ...
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1answer
47 views

1D Ising model and degenerate states

I am studying the Ising model in 1D, in the absence of magnetic interaction but in presence of an external magnetic field. The Hamiltonian for an Ising chain with $n$ sites is hence described by $$H = ...
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1answer
40 views

Coset construction of Tricritical Ising CFT

In http://iopscience.iop.org/1742-5468/2008/03/P03010 the authors state that the Tricritical Ising Model (TIM) CFT can be obtained from a Wess Zumino Witten construction based in the coset ...
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3answers
70 views

Entropy change in an irreversible process between 2 equilibrium state

Calculating entropy change in an irreversible process between 2 states requires computing the change in entropy for any reversible process between the 2 same states, but why? If someone could provide ...
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1answer
35 views

Spin correlation function identity

The correlation function G between two spins is usually defined as $$ G=\langle \sigma_a \sigma_b\rangle - \langle \sigma_a\rangle \langle\sigma_b\rangle $$ The $\sigma$ are the value of the spins ...
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1answer
117 views

Can I use the grand canonical ensemble for a photon gas?

I have been reading about photon gases at https://www2.chem.utah.edu/steele/doc/chem7040/chandlerch4.pdf. They do the analysis using a canonical ensemble. Since photon numbers are not conserved, I ...
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23 views

how will the distribution of the no. of particles be in a system ,(N,V,E) if N tends to infinity?

MB distribution is followed if there are N no. of non interacting and distinguishable particles. But if N tends to infinity why does the no. of micro states reduces? Is there any peak in the graph?
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34 views

Does spin degeneracy affect ideal Fermi gases in any way as T->Infinity?

In other words, given any system comprised of an ideal Fermi gas, in the high-temperature (classical) limit, are there any observable thermodynamic quantities (pressure, volume, energy, density, etc.) ...
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1answer
41 views

What is the gas entropy as a functional of a one-particle distribution function?

There are some discrepancies on how to introduce entropy in classical kinetic theory. In what follows $f(r,p,t)$ is the usual one-particle distribution function of a monatomic gas, normalised to the ...
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1answer
41 views

Reference about probability to study statistical mechanics

I've started studying statistical mechanics but I feel that I need to understand probability better. There are tons of books on probabilities out there, but some of them just talk too much, with tons ...
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34 views

Number of particles in a box at thermal equalibrium

Consider a cube box of volume $V$ in thermal equilibrium at temperature $T$. We have 3 pieces of information: The probability of finding a particle of mass $m$ in the box having momentum in ...
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1answer
204 views

What happens in a gas of magnets?

This SMBC comic asks what happens if you make a gas of magnetic particles: I was wondering whether anyone has run into actual examples of this or something like it. A classical example similar to ...
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45 views

Landau's derivation of the law of entropy increase - clarification

In Landau&Lifshitz V: Statistical Physics the following derivation of the law of increase of entropy is given. I need help understanding several crucial steps; I'll briefly summarize the notations ...
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2answers
51 views

What is the theoretical instantaneous temperature of a gas?

When we measure the temperature of a gas we typically integrate the molecular collisions and wind up with an 'average' temperature due to the sensor comprising a relatively large thermal mass. And ...
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1answer
74 views

Partition function: Number of states? Doesn't add up for ising

While trying to really understanding the partition function in statistical mechanics, I tried looking at it for a 2D ising model, as that's been helpful for me for all kinds of thermodynamic values. ...
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1answer
46 views

Definition of quantum microcanonical ensemble in Landau&Lifshitz

I'm reading the first chapters of Landau&Lifshitz 's [Statistical Physics][1] and I don't understand the definition of the quantum microcanonical ensemble. The microcanonical distribution for a ...
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1answer
36 views

What is quantum states of a gas? Is it the principle quantum no.?

When we write that the possible quantum states of a system are $S=1,2,3.\dots$, how is that related with the four quantum numbers, especially with the spin of a particle? Also according to BE ...
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37 views

Chemical reaction A+B$\leftrightarrow$C. Equilibrium VS Non Equilibrium

Could you please confirm or say why I am wrong? Let us consider the steady state of the chemical reaction $A+B \leftrightarrow^{k_+}_{k_-} C$, with $k_+$ and $k_-$ the forward and backward rates. ...
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1answer
110 views

Number $g(T)$ of relativistic degrees of freedom as a function of temperature $T$

Let us consider the total number of relativistic degrees of freedom $g(T)$ for particle species in our universe: $$g(T)=\left(\sum_Bg_B\right)+\frac{7}{8}\left(\sum_Fg_F\right)$$ Where the sums are ...
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45 views

What is the use of Schwinger-Keldysh formalism?

In non-equilibrium statistical mechanics, there is this formidable formalism, called the Schwinger-Keldysh formalism. I have read about it, and I understand what it is. However, what I what to know ...
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27 views

Time evolution of the density of phase points for an ensemble

I want to calculate the time evolution of the density of phase points for an ensemble of N harmonic oscillators. However, I intended to do so without using the Liouville equation. Sure, I want to ...
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1answer
50 views

Is Boltzmann constant $k_B$ constant?

I heard in a lecture that Boltzmann constant $k_B$ is not constant in some special cases. Do you know the title of the article which contains this one? Do you think this idea is true?
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28 views

Debye-Huekel Theory and the continuum approximation

This question stems from a problem I was doing on the Debye-Hueckel theory. It says that the continuum approximation which underlies the Debye-Hueckel theory is valid provided that $\lambda_D \gg ...
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1answer
50 views

Why is the number of phonon modes in a solid restricted to a finite value?

Kittel's Thermal Physics (Amazon link) makes the statement: There is no limit to the number of possible electromagnetic modes in a cavity, but the number of elastic modes in a finite solid is ...
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46 views

Corrections to the Equipartitio theorem

Does anyone know why sometimes $E = \frac{3}{2}k_{b}T $ is written as $E = \pi k_{b}T$. Where does this come from?
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1answer
60 views

Understanding summations over microstates of a given function

I am struggling to understand how to sum over microstates in statistical mechanics. Consider an $N$-spin system where $N \gg 1$ and $\Gamma=\{n_i \}$ for $1 \leq i \leq N$ and each $n_i$ is equal ...
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1answer
40 views

Meaning of Strongly and Weakly Degenrate

In ideal Bose and Fermi gases we often use Either Strongly Degenerate Ideal Bose/Fermi or Weakly Degenerate Ideal Bose/Fermi gas. As far as I know mathematically if the fugacity $z=e^{\beta\mu}$ close ...
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1answer
110 views

Does a vacuum, suddenly opened, become hotter than its surroundings?

Suppose you have an insulated container that is equipped with a valve to let air in. Initially the container is evacuated. You then quickly open the valve, allowing air to rush in. What is the ...
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1answer
105 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
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1answer
44 views

2 level atomic system interacting with Black body radiation. Relaxation time issue

I am studying the transient regime of a 2 level atomic system ($N_1,N_2$) interacting with a blackbody radiation from a source at constant temperature $T_{nr}$. The initial state of the atomic system ...
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1answer
89 views

Calculating the entropy of a monatomic ideal gas

I am looking at the start of the consider how to calculate the entropy of a monatomic ideal gas. We need to determine the number of microstates in $E \leq \mathcal{H}(\Gamma) \leq E+\Delta$. The ...
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1answer
124 views

What does a correlation function measure and how does it do this mathematically?

I would really appreciate if someone could explain. What does a correlation function like a density-density correlation function $$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$ ...
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1answer
40 views

Why does this derivation of the dependence of free energy on pressure not work?

It is well known that the Gibbs Free Energy of a gas depends on the pressure via the following formula: $$G_m(p) = G^\circ_m + RT\ln{\frac{p}{p^{\circ}}}$$ Where $G_m$ is the molar gibbs free energy ...
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2answers
65 views

According to Liouville's theorem, why is the measure on an energy-surface different from the measure on the phase space in general

I recently read Khinchin's derivation of Liouville's theorem. I was able to follow the math for the most part, however I was hoping for an intuitive understanding about why the form of the measure on ...
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1answer
19 views

What is an expression/physical law that relates high frequency thermal fluctuations to gas pressure?

When a gas is compressed the 'ideal gas law' can predict what the increase in gas temperature will be. But that's just a mean temperature, right? At a quantum level the frequency of molecular ...
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1answer
22 views

Bose-Einstein phase transition and average number of part in state l

The explanation I have trouble understanding is this: The average number of particles $<n_l>$ on state $l$ is $$<n_l>=\frac{z}{e^{\beta \epsilon_l}-z}$$ where $z=e^{\beta \mu '}$ is the ...
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2answers
125 views

Why is most probable speed not equal to rms speed for an ideal gas?

The rms speed of ideal gas is $$\mathit{v_{rms}} = \sqrt{\dfrac{3RT}{M}}.$$ The most probable speed is the speed where $\dfrac{dP(\mathit {v})}{dv} =0$ where $P(\mathit{v})$ is the probability ...
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2answers
82 views

Simplest example of spontaneous breaking of time reversal symmetry

Consider a two-dimensional fluid flow, confined to a square, where the bottom is held at a higher temperature than the top. With appropriate choices of the parameters, this will form a single ...
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1answer
41 views

Is there an equivalent probability distribution for fermions and bosons to the expression for distinguishable particles

So the particle distribution of two particles is simply $$ P_{12}=P_1(r_1)P_2(r_2) $$ where $ P_{12}$ is simply the modulus of the total wavefunction squared and $ P_1 $ and $ P_2$ are the the ...
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1answer
34 views

Number of states of a simple system

I am trying working on a problem in which there are two energy states $E_{1}<E_{2}$, and three different (i.e. distinguishable) particles. I cannot decide if the order of the particles matters. ...
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2answers
67 views

Temperature in statistical mechanics and differentiating entropy

In statistical mechanics, the entropy of an isolated system with energy $E$ (with fixed volume $V$ and chemical composition $N$) is defined as $S(E) = k \log \Omega$, where $\Omega$ is the number of ...
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112 views

What exactly happens at the second-order phase transition of the 2D Toric code?

For a 2D Toric code specified by $$H = -J_s\sum_{s} \prod_{j\in s} \sigma^x_j - J_p\sum_{p} \prod_{j\in p} \sigma^z_p - h_x\sum_{l} \sigma^x_l - h_z\sum_{l} \sigma^z_l$$ where $s$ denotes stars, $p$ ...
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45 views

Difference between molecular dynamics and direct simulation Monte Carlo

I just started studying about rarefied gases and I came across the concepts of Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC); so here is my question: How are these two fields ...
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1answer
39 views

Show that, for two large systems in thermal contact, the number $\Omega^{0}(E^{0},E_1)$ can be expressed as a Gaussian in the variable $E_1$

This problem below is from the book "Statistical Mechanics" by Pathria. The author defined the number of microstates of a system with two subsystems exchanging energy as: $$\Omega_1(E_1) ...
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32 views

How to understand the Bose glass phase has infinite superfluid susceptibility?

The Bose glass phase is characterized by a gapless excitation spectrum, exponential decay of superfluid correlations, finite compressibility and infinite superfluid susceptibility. The disordered ...
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41 views

grand-canonical ensemble

I was wondering if the following reasoning is correct for example for electrons in the classical or qm grand-canonical ensemble? Is it always valid in the grandcanonical ensemble to calculate the ...
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45 views

How to apply Wick's theorem in 2nd quantization for Spin Density Operators?

I am trying to work out a correlation function consisting of two spin density operators. Once I rewrite everything in 2nd quantized form, I am unsure of how to apply wicks theorem because the paul ...